I do have a few retro modems, too. And an acoustic coupler.
My goal is to use them for my video channel one day, to simulate the experience of playing old modem chess games in the old days.
To do so, I've got an old Auerswald unit. It's essentially an internal landline, with multiple telephone connections and a simulated dial tone.
By dialing zero (0), you can leave the internal system and connect your telephone to the real landline.
The English term for such an apparatus is "private branch exchange" (PBX), according to the web.
Essentially, modem play is an alternative to the null-modem option that many games supported.
Second purpose is to dial into re-creations of classic online services.
Fans of old systems such as Minitel, BTX or AOL have their PCs connected to their VOIP DSL/Cable router modems.
An example of such a thing is "Neu Ulm", here in Germany.
Then, there is old mailbox software that wants to see a modem.
Some of them have interesting games built-in..
Last, but not least, there are still a few mailbox systems around.
Some don't even have an internet connection, it seems.
I suppose that's on purpose, even.
Edit: Old modems are very interesting. They contain a little computer, sometimes based on rare micro-controllers.
Even if they have a permanent ROM that can't be modified, many can be wired to accept an external EPROM.
So it's worth not throwing them out. New modems are also interesting if they have a DSP chip.
Such a chip could be repurposed for other hardware projects, maybe.
Edit: Photo attached.
"Time, it seems, doesn't flow. For some it's fast, for some it's slow.
In what to one race is no time at all, another race can rise and fall..." - The Minstrel
//My video channel//